Zacli on Repeating Circles. 355 



ficiently evident from the confesoions lie made in his letters to 

 M. Borda, the inventor, and consequently the ardent partisan, 

 of the circles which bear his name/ 



In one of his letters deposited in the Royal Observatory at 

 Paris, he writes as follows : — 



" I send you tables of the results of my cursed observations 

 of the pole-stai', and of /3 UrsiE Minoris. You will see abundant 

 proofs that I am incapable of making observations of latitude 

 even passable ; I am in despair at it. The pole-star was ob- 

 served with one of two circles ; /3 Ursce Minoris with the other. 

 I used as much care as heretofore, and even more ; the verti- 

 cality of the circle was verified every day ; the level proved that 

 it did not vary half a minute in the course of a day's obser- 

 vation. 



" The position of the vernier was inspected eveiy time before 

 we began, to see that it had not changed since the last observa- 

 tion ; the level was adjusted with every possible precaution ; I 

 pointed to the star with all the accuracy of which I am master; 

 never did I take so many precautions, and never did I succeed 

 so ill. I turned the circle again and again in all directions ; I 

 examined all the pieces; I tried to discover the cause of these 

 monstroas discordances, and I could discover nothing, although 

 I consumed an infinity of time about it. It is then, evidently, 

 my awkwardness. I was greatly distressed when the results 

 of one day differed from those of another by 1" or 2", though 

 this is a degi'ee of precision not always attained with an excel- 

 lent mural circle of eight feet, and not exceeded in zenith 

 distances for the measm-ement of degrees made with the best 

 and the largest sectors. 



" In the present case, I presumed that a small number of 

 observations above and below the pole, would not leave me an 

 uncertainty of more than two or three tenths of a second. So far 

 am I from realizing these expectations, that I have deviations 

 of 10", and the mean of the fii'st series differs from the mean 

 of the second. I have lost all my time in revising and calcu- 

 lating these observations ; and after having neglected another 

 undertaking in the hope of accomplishing this, I have obtained 

 nothing but the certainty of the worst possible success." 



M. Delambre adds still further (p. 270), " What then hap- 

 pened to him (M. Mcchain) had happened to me four times at 

 Dunkirk ; and although I did not distress myself like him, I 

 liad, like him, redoubled my precautions against failure. In 

 relating his own history he relates mine, and our example may 

 console other astronomers who may experience similar disap- 

 pointments." 



It nuist be confessed, that however consolatory this may be 

 Y V 2 to 



